Beyond the nukes another comment mentioned, the UK is also a permanent UN Security Council member, a founding NATO member and a productive member of the Five Eyes and AUKUS [1]. And it still has the world's fifth most powerful navy [2].
> substantial colonial possessions
No, but they have overseas military installations in Gibraltar and on Cyprus, the Falkland Islands and Diego Garcia. Smaller installations at Ascension Island, in Singapore and Brunei "provide important staging posts and logistical support facilities for British and allied forces passing nearby" [3]. In terms of practical force projection radius, they're in a very small club of nations.
[1] https://en.wikipedia.org/wiki/British_Armed_Forces#cite_note...
[2] https://worldpopulationreview.com/country-rankings/largest-n...
[3] https://www.europarl.europa.eu/meetdocs/2004_2009/documents/...
That, in and of itself, is worth a lot -- potentially even more than having a large military.
I think most of UK public would consider that a prime minister that plans using nukes in offensive capacity belong in a padded cell.
They are so unbelievably powerful it blows my mind.
https://worldpopulationreview.com/country-rankings/military-...
At #5 world-wide by expenditure this may be a bit over-stated. Or else "vast military" is just a standin for "US or China".
